We can consider the side whose length is 12.8 inches as the base. However, we need to find the height. To do so, we will pay close attention to the right triangle formed by the height, a side, and a part of a nonparallel side.
We can see that the measure of two of the interior angles of the triangle are 45^(∘) and 90^(∘). We can use the Triangle Angle Sum Theorem to find the measure of the third angle.
180^(∘)- 90^(∘)- 45^(∘)=45^(∘)
The third angle measures 45^(∘) and, therefore, we have a 45^(∘)-45^(∘)-90^(∘) triangle. In this type of triangle, the legs are congruent and the length of each leg is sqrt(2)2 times the length of a hypotenuse. With this information, and knowing that the length of the hypotenuse is 6.4 inches, we can find the length of both legs of the triangle.
Leg: sqrt(2)/2 * 6.4=3.2sqrt(2)
Therefore, the height of the parallelogram is 3.2sqrt(2)in.
Now that we know that the base is 12.8 inches and that the height is 3.2sqrt(2) inches, we can substitute these values in the formula for the area of a parallelogram.
